Two-Tailed Hypothesis

Definition

A two-tailed hypothesis is a statistical hypothesis test in which the critical region is two-sided, meaning it is split into two parts, one in each of the tails of the probability distribution. This type of hypothesis test is used when the researcher is interested in determining if the population parameter is different from a specified value, without specifying the direction of the difference.

5 Must Know Facts For Your Next Test

1. In a two-tailed hypothesis test, the null hypothesis states that the population parameter is equal to a specified value, while the alternative hypothesis states that the population parameter is not equal to that value.
2. The critical region for a two-tailed hypothesis test is split into two parts, one in each of the tails of the probability distribution, with each tail representing a specified level of significance (typically 0.025 for each tail, resulting in an overall significance level of 0.05).
3. Two-tailed hypothesis tests are appropriate when the researcher is interested in determining if the population parameter is different from a specified value, but does not specify the direction of the difference.
4. The test statistic for a two-tailed hypothesis test is compared to the critical values in both tails of the probability distribution to determine if the null hypothesis should be rejected or fail to be rejected.
5. Two-tailed hypothesis tests are more conservative than one-tailed hypothesis tests, as they require a larger test statistic to reject the null hypothesis, due to the split critical region.

Review Questions

• Explain the purpose of a two-tailed hypothesis test and how it differs from a one-tailed hypothesis test.
  • The purpose of a two-tailed hypothesis test is to determine if the population parameter is different from a specified value, without specifying the direction of the difference. This is in contrast to a one-tailed hypothesis test, which is used to determine if the population parameter is greater than or less than a specified value. The key difference is that a two-tailed test has a critical region split into two parts, one in each tail of the probability distribution, while a one-tailed test has the critical region located entirely in one tail of the distribution. This makes the two-tailed test more conservative, as it requires a larger test statistic to reject the null hypothesis.
• Describe the relationship between the null and alternative hypotheses in a two-tailed hypothesis test.
  • In a two-tailed hypothesis test, the null hypothesis ($H_0$) states that the population parameter is equal to a specified value, while the alternative hypothesis ($H_1$ or $H_a$) states that the population parameter is not equal to that value. This means that the alternative hypothesis is a two-sided statement, indicating that the population parameter could be either greater than or less than the specified value. The null hypothesis is the statement that the researcher is trying to disprove or fail to reject, while the alternative hypothesis is the statement that the researcher is trying to support through the statistical analysis.
• Evaluate the implications of using a two-tailed hypothesis test versus a one-tailed hypothesis test in the context of 9.1 Null and Alternative Hypotheses.
  • The choice between a two-tailed and one-tailed hypothesis test in the context of 9.1 Null and Alternative Hypotheses depends on the research question and the researcher's expectations. A two-tailed test is appropriate when the researcher is interested in determining if the population parameter is different from a specified value, without specifying the direction of the difference. This is a more general and exploratory approach, as it allows for the possibility of the population parameter being either greater than or less than the specified value. In contrast, a one-tailed test is appropriate when the researcher has a specific directional expectation, such as the population parameter being greater than or less than a specified value. The choice between these two approaches should be guided by the research question, the existing knowledge or theory, and the potential implications of the findings.

Related terms

Null Hypothesis: The null hypothesis (denoted as $H_0$) is a statement that the population parameter is equal to a specified value. It is the hypothesis that the researcher is trying to disprove or fail to reject.

Alternative Hypothesis: The alternative hypothesis (denoted as $H_1$ or $H_a$) is a statement that the population parameter is not equal to the value specified in the null hypothesis. It is the hypothesis that the researcher is trying to support.

One-Tailed Hypothesis: A one-tailed hypothesis is a statistical hypothesis test in which the critical region is one-sided, meaning it is located entirely in one tail of the probability distribution. This type of hypothesis test is used when the researcher is interested in determining if the population parameter is greater than or less than a specified value.